Embedding Deduction Modulo into a Prover
Deduction modulo consists in presenting a theory through rewrite rules to support automatic and interactive proof search. It induces proof search methods based on narrowing, such as the polarized resolution modulo. We show how to combine this method with more traditional ordering restrictions. Interestingly, no compatibility between the rewriting and the ordering is requested to ensure completeness. We also show that some simplification rules, such as strict subsumption eliminations and demodulations, preserve completeness. For this purpose, we use a new framework based on a proof ordering. These results show that polarized resolution modulo can be integrated into existing provers, where these restrictions and simplifications are present. We also discuss how this integration can actually be done by diverting the main algorithm of state-of-the-art provers.
KeywordsInference Rule Atomic Proposition Sequent Calculus Ground Term Empty Clause
Unable to display preview. Download preview PDF.
- 1.Bachmair, L.: Proof normalization for resolution and paramodulation. In: Dershowitz, N. (ed.) RTA 1989. LNCS, vol. 355, pp. 15–28. Springer, Heidelberg (1989)Google Scholar
- 7.Dowek, G.: Polarized resolution modulo (2010) (to be presented at IFIP TCS)Google Scholar
- 10.Dowek, G., Miquel, A.: Cut elimination for Zermelo’s set theory (2006), available on authors’ web pageGoogle Scholar
- 12.Dowek, G., Werner, B.: Arithmetic as a theory modulo. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 423–437. Springer, Heidelberg (2005)Google Scholar
- 13.Goubault-Larrecq, J.: A note on the completeness of certain refinements of resolution. Research Report LSV-02-8, Laboratoire Spécification et Vérification, ENS Cachan, France (2002)Google Scholar
- 14.Hermant, O.: Méthodes Sémantiques en Déduction Modulo. Ph.D. thesis, École Polytechnique (2005)Google Scholar
- 17.Plotkin, G.: Building in equational theories. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence, vol. 7, pp. 73–90. Edinburgh University Press, Edinburgh (1972)Google Scholar